ABSTRACT
For the next theorem and its associated results we assume tllat the Ustatistic U;, is constructed using i.i.d. random variables. However; with minor modifications in the proof the same results hold true for the case of random variables which arc not necessarily identically distributed, as long as the kernel h(X, , , . . . , X,",,) is uniforrnly bounded below and above and has the same expectation for every choice of { i l , . . . ;i,, } from {l,. . . , n,}.
